God said, “Let mathematics be beautiful” and hence came figures like the one showcased above. And henceforth this angel has been continuously en-captivating people like me. This is truly a source of seamless beauty and in truest sense a joy forever. Welcome to the world where the harder you analyse, the richer the object becomes… Welcome my dear friends, to the world of fractals…

I hope that the title figure has already invoked curiosity if not amazement in your minds. But you are right; isn’t it just another picture? I bet, it can be anything but not ‘yet another picture’. Here is the reason; zoom into any boundary of the picture, and you get…

and further in…

Keep going!

And finally after zooooooming into one little corner you would see

 

A miniature Mandelbrot.

And take my word for it – the whole of the first figure (the original Mandelbrot) is composed of infinitely many miniatures of itself.

What is even more fascinating is that such figures have a family of their own – figures composed of miniature copies of themselves. Here I showcase a few more of their kind

 

The Newton Fractal

The Julia Set

The Sierpinski Carpet

Zoom into them and let your imaginations fly

To know more about these mathematical beauties, you can have a look at a presentation given by me (and my friends) on this topic FRACTALLY SPEAKING

Or you could do through this general article by me Fractal Article